CFA Program — Fixed Income

Question 1

Prepayment risk is most relevant to which type of fixed income security?

• A) Zero-coupon government bonds
• B) Mortgage-backed securities, where underlying borrowers may repay principal earlier than scheduled
• C) Fixed-rate corporate bonds with no call feature
• D) Treasury bills

Question 2

A bond's effective duration, as opposed to modified duration, is generally the more appropriate measure of interest rate sensitivity for bonds with:

• A) No embedded options, such as plain vanilla bonds
• B) Embedded options (e.g., callable or putable bonds), since their cash flows can change as interest rates change
• C) Zero coupon structure only
• D) Fixed cash flows regardless of interest rate changes

Question 3

A collateralized debt obligation (CDO) that pools debt securities and issues multiple tranches with differing risk/return profiles typically allocates losses:

• A) Equally across all tranches regardless of seniority
• B) First to the most senior tranche
• C) First to the most subordinate (equity/junior) tranche, with senior tranches absorbing losses only after junior tranches are exhausted
• D) Randomly among all tranches

Question 4

The option-adjusted spread (OAS) on a callable bond, compared to its simple nominal spread over a benchmark, is generally:

• A) Higher than the nominal spread, since it adds back the value of the option
• B) Lower than the nominal spread, since it removes the compensation embedded in the spread for the value of the issuer's call option
• C) Always exactly equal to the nominal spread
• D) Undefined for callable bonds

Question 5

A key-rate duration measures a bond's price sensitivity to:

• A) A parallel shift in the entire yield curve only
• B) A change in a specific point (maturity segment) along the yield curve, holding other maturities constant
• C) Changes in the bond's credit rating only
• D) Changes in the bond issuer's stock price

Question 6

In securitization, the process of tranching cash flows to create securities with different levels of credit risk is primarily intended to:

• A) Eliminate all credit risk from the underlying collateral pool
• B) Redistribute the credit risk of the underlying pool across tranches with different risk/return profiles to appeal to different investor risk appetites
• C) Guarantee identical yields across all tranches
• D) Convert the underlying assets into equity securities

Question 7

An analyst decomposes a bond's expected return into yield income, rolldown return, expected currency gain/loss, and expected credit gain/loss. This decomposition is most useful for:

• A) Understanding the specific sources of a bond's expected total return, helping identify which factors are driving the investment's risk and return profile.
• B) Guaranteeing the bond will achieve a specific total return.
• C) Eliminating the need to consider interest rate risk entirely.
• D) Determining the bond's legal maturity date.

Question 8

"Rolldown return" for a bond held in a portfolio, assuming a stable, upward-sloping yield curve, refers to:

• A) A return that only occurs when yield curves are inverted.
• B) A form of currency risk unrelated to interest rates.
• C) A guaranteed negative return for any bond investor.
• D) The price appreciation a bond experiences as it "rolls down" the yield curve toward maturity, assuming the yield curve's shape remains unchanged, since shorter-maturity points typically have lower yields.

Question 9

A collateralized loan obligation (CLO) is a structured credit product primarily backed by:

• A) A single government bond.
• B) A pool of equity securities exclusively.
• C) A pool of leveraged corporate loans.
• D) A pool of residential mortgages exclusively.

Question 10

An analyst evaluating a high-yield corporate bond's credit risk examines the issuer's "recovery rate" expectations in the event of default. A higher expected recovery rate, all else equal, would generally result in:

• A) A guarantee that default will never actually occur.
• B) A lower required credit spread, since bondholders expect to recover more of their investment even if default occurs.
• C) A higher required credit spread, regardless of expected recovery.
• D) No effect on the required credit spread whatsoever.

Question 11

Which of the following best describes the "key rate duration" approach to measuring interest rate risk, as compared to effective duration alone?

• A) Key rate duration measures sensitivity to changes at specific points along the yield curve, providing more granular insight into a bond or portfolio's exposure to non-parallel yield curve shifts, which a single effective duration measure cannot fully capture.
• B) Key rate duration measures only a portfolio's currency risk, unrelated to interest rates.
• C) Key rate duration and effective duration always produce identical risk assessments in every scenario.
• D) Key rate duration is only relevant for equity portfolios, not fixed income.

Question 12

A portfolio manager implementing a "bullet" bond structure versus a "barbell" structure with the same overall duration would generally expect, all else equal, that the bullet structure has:

• A) Higher convexity than the barbell structure in every case.
• B) Identical convexity to the barbell structure at all times.
• C) No relationship between structure and convexity whatsoever.
• D) Lower convexity than the barbell structure, since concentrating maturities reduces the dispersion of cash flows compared to spreading them across short and long maturities.

Question 13

A bond portfolio manager's "credit barbell" strategy involves combining high-quality, low-risk bonds with a smaller allocation to higher-yielding, higher-risk credits, rather than holding entirely intermediate-quality credit. A primary motivation for this approach could be:

• A) Seeking to capture some of the higher yield available from riskier credits while maintaining an overall conservative average credit quality, potentially offering more favorable risk-adjusted characteristics than a uniform intermediate-quality allocation.
• B) Guaranteeing the portfolio will never experience any credit losses.
• C) This strategy always underperforms a uniform intermediate-credit-quality portfolio in every scenario.
• D) A strategy that has no relationship to portfolio risk or return characteristics.

Question 14

An analyst decomposes a portfolio's historical fixed-income return relative to its benchmark, finding that most of the excess return came from sector allocation decisions rather than security selection or duration positioning. This type of analysis is best described as:

• A) Yield curve construction
• B) Fixed-income performance attribution
• C) Option-adjusted spread analysis
• D) Key rate duration calculation

Question 15

An analyst evaluating emerging market sovereign bonds notes that local-currency-denominated bonds and hard-currency (such as USD)-denominated bonds issued by the same country often trade at different yields. Which of the following best explains a key driver of this yield differential?

• A) Local-currency bonds carry additional currency risk for foreign investors (since local currency depreciation would reduce returns when converted back to a hard currency), which is compensated through a different yield level compared to hard-currency bonds that eliminate this specific currency risk for the investor.
• B) Local-currency and hard-currency bonds from the same issuer always carry identical risk and should always trade at identical yields.
• C) Currency denomination has no effect on bond yields under any circumstances.
• D) Hard-currency bonds always carry more risk than local-currency bonds issued by the same country.

Question 16

Which of the following best describes the primary risk consideration for an investor holding a floating-rate note issued by a financial institution that includes a contractual "bail-in" provision?

• A) Bail-in provisions have no relevance to bank-issued debt securities.
• B) In the event the issuing institution faces severe financial distress, the bail-in provision could convert the bondholder's debt claim into equity (or otherwise impose losses), potentially subordinating what would traditionally be a senior creditor claim.
• C) Bail-in provisions guarantee bondholders will always be repaid in full regardless of the issuer's condition.
• D) Bail-in provisions apply only to equity securities, never to bonds.

Question 17

An analyst is comparing the relative value of two similarly-rated corporate bonds using Z-spread (zero-volatility spread) rather than simple nominal spread. The primary advantage of using Z-spread is:

• A) Z-spread ignores the bond's cash flow timing entirely.
• B) Z-spread applies only to bonds with embedded options, never to option-free bonds.
• C) Z-spread measures the constant spread that must be added to each point on the entire benchmark spot rate curve to make the bond's discounted cash flows equal its market price, providing a more precise measure than a simple nominal spread calculated against a single benchmark point.
• D) Z-spread and nominal spread always produce identical values for every bond.

Question 18

Which of the following best describes the primary difference between a "top-down" and "bottom-up" approach to fixed-income portfolio construction?

• A) Top-down and bottom-up approaches are functionally identical with no meaningful distinction.
• B) A bottom-up approach never considers any individual security characteristics.
• C) A top-down approach can only be used for equity portfolios, never fixed income.
• D) A top-down approach begins with macroeconomic and sector-level views to set overall positioning, then selects individual securities within that framework, while a bottom-up approach focuses primarily on identifying attractive individual securities based on issuer-specific analysis.

Question 19

A portfolio manager uses a binomial interest rate tree to value a putable bond. The put option value is $3.50. The straight bond value is $98.00. The value of the putable bond is:

• A) $94.50
• B) $98.00
• C) $101.50
• D) $3.50

Question 20

Under the arbitrage-free valuation framework, a bond's value equals:

• A) The present value of all cash flows discounted at the bond's YTM
• B) The sum of present values of each cash flow discounted at the corresponding spot rate
• C) The present value of coupons discounted at the risk-free rate
• D) The par value adjusted for credit spreads

Question 21

A fixed-income portfolio manager uses key rate durations. She finds that her portfolio has a large positive key rate duration at the 10-year point. This means the portfolio is most vulnerable to:

• A) A parallel upward shift in the yield curve
• B) A rise in 10-year yields specifically
• C) A flattening of the yield curve
• D) Widening credit spreads across all maturities

Question 22

Effective duration differs from modified duration for bonds with embedded options because:

• A) Effective duration uses yield to maturity while modified duration uses spot rates
• B) Effective duration captures the change in cash flows due to option exercise
• C) Modified duration is always longer than effective duration
• D) Effective duration applies only to floating-rate bonds

Question 23

A corporate bond has a Z-spread of 200 bps and an OAS of 150 bps. The value of the embedded option is closest to:

• A) 200 bps
• B) 150 bps
• C) 50 bps
• D) 350 bps

Question 24

The credit valuation adjustment (CVA) in fixed income represents:

• A) The spread added to the risk-free rate to price a corporate bond
• B) The present value of expected losses due to default
• C) The markup applied by dealers to bond transaction prices
• D) The adjustments made to mark a bond portfolio to market

Question 25

A bond has a modified duration of 7.5. If market yields rise by 50 basis points, the bond's price is expected to change by approximately:

• A) +3.75%
• B) -7.50%
• C) -0.50%
• D) -3.75%

Question 26

Convexity adjustment improves upon a duration-only estimate of a bond's price change primarily because:

• A) Duration already perfectly captures the bond's price-yield relationship without any error.
• B) Convexity is only relevant for bonds with embedded options, never for option-free bonds.
• C) Duration alone assumes a linear price-yield relationship, while the actual relationship is curved (convex), so incorporating convexity captures this curvature and improves accuracy, especially for larger yield changes.
• D) Convexity eliminates all interest rate risk entirely.

Question 27

A bond has positive convexity. All else equal, this characteristic is generally:

• A) Only possible for bonds with embedded call options.
• B) Beneficial to the bondholder, since it means the bond's price rises more for a given yield decrease than it falls for an equivalent yield increase.
• C) Harmful to the bondholder under all circumstances.
• D) Irrelevant to the bondholder's total return.

Question 28

A callable bond can exhibit "negative convexity" at low yield levels because:

• A) As yields fall, the issuer's incentive to call the bond increases, capping the bond's potential price appreciation (the price rise is limited relative to an otherwise identical option-free bond).
• B) Callable bonds always have identical price behavior to option-free bonds at every yield level.
• C) The issuer is required to increase the coupon rate as yields fall.
• D) Negative convexity means the bond's price becomes negative.

Question 29

The option-adjusted spread (OAS) on a callable bond, compared to its simple yield spread over a benchmark, is intended to:

• A) Ignore credit risk entirely, focusing only on the embedded option.
• B) Always be identical to the nominal spread, regardless of the option.
• C) Apply exclusively to option-free bonds.
• D) Remove the effect of the embedded call option from the spread, providing a spread measure that reflects only credit and liquidity risk, comparable across bonds with different embedded options.

Question 30

A collateralized mortgage obligation (CMO) is created by:

• A) Eliminating prepayment risk entirely for every investor in the structure.
• B) Guaranteeing an identical yield across all tranches, regardless of risk.
• C) Redirecting the cash flows from a pool of mortgages into different tranches with varying risk, maturity, and prepayment characteristics.
• D) Issuing a single bond with identical characteristics to every underlying mortgage.

Question 31

A 2-year, annual-pay, 5% coupon bond with a $100 face value is callable at par ($100) at the end of Year 1 only. A binomial interest rate tree calibrated to the benchmark curve shows a Year 1 one-year rate of 5.0%, and Year 2 one-year forward rates of 6.0% (up state) and 4.0% (down state), each with equal (50%) probability. Using backward induction and assuming the issuer calls the bond whenever its computed value exceeds the $100 call price, the callable bond's value today is closest to:

• A) $100.01, which is the value of the otherwise identical non-callable (straight) bond -- this result incorrectly ignores the issuer's call option entirely by failing to cap the down-node value at the $100 call price.
• B) $100.96, which incorrectly uses only the down-node value (before applying the call price cap) as if it were the bond's value today, without performing the full backward induction across both nodes and discounting to the present.
• C) $95.24, which incorrectly discounts the Year 2 cash flow using only the 2-year spot rate in a manner inconsistent with the binomial tree's up/down forward rates and call feature.
• D) $99.55: At Year 2 (maturity), the cash flow is $105 in both states. Value at the up node = 105/1.06 = $99.06 (not called, since below $100). Value at the down node = 105/1.04 = $100.96, but since this exceeds the $100 call price, the issuer calls the bond, so the down-node value used is capped at $100. Value today = [0.5 x (99.06 + 5) + 0.5 x (100 + 5)] / 1.05 = [52.03 + 52.50] / 1.05 = $99.55.

Question 32

An analyst is comparing a callable corporate bond to an otherwise identical non-callable bond of similar credit quality using both Z-spread and option-adjusted spread (OAS) measures. The OAS for the callable bond is notably lower than its Z-spread. What does this most directly reflect?

• A) The OAS removes the value of the embedded call option from the spread, isolating the compensation for credit and liquidity risk; since the call option benefits the issuer (at the bondholder's expense) and therefore has positive value to the issuer, the OAS (spread net of the option's value) is lower than the Z-spread (which includes compensation the investor appears to receive for bearing the option risk without removing the option's cost).
• B) The OAS and Z-spread should always be identical for a callable bond, and any observed difference necessarily indicates a data or calculation error.
• C) A lower OAS than Z-spread indicates the bond is putable rather than callable, since put options are assumed to always increase, rather than decrease, the OAS relative to the Z-spread.
• D) The OAS calculation ignores interest rate volatility entirely, while the Z-spread properly incorporates it, the reverse of their actual construction, since OAS is specifically derived using an interest rate tree calibrated to volatility.

Question 33

An analyst compares the Z-spread and the nominal (yield) spread for a specific corporate bond relative to the Treasury curve and finds that the Z-spread is meaningfully lower than the nominal spread. This is most likely because:

• A) The Z-spread and nominal spread are calculated using identical methodologies and should always be exactly equal for every bond regardless of the shape of the yield curve.
• B) The Z-spread ignores the bond's coupon and cash flow timing entirely, while the nominal spread properly accounts for the full cash flow schedule, the reverse of their actual construction.
• C) A lower Z-spread than nominal spread always indicates the bond contains an embedded put option, which is the only possible explanation for any divergence between the two measures.
• D) The Z-spread is calculated as the constant spread added to each point on the entire benchmark spot rate curve needed to make the present value of the bond's cash flows equal its market price, whereas the nominal spread simply compares the bond's yield to maturity to a single point on the par yield curve of similar maturity; the two measures typically diverge more when the benchmark yield curve is steeply sloped.

Question 34

A bond has an effective duration of 7.5 and effective convexity of 85. If the bond's yield is expected to rise by 100 basis points, the estimated percentage change in the bond's price, using both duration and convexity, is closest to:

• A) -7.50%, which incorrectly uses only the duration effect and omits the convexity adjustment term entirely, understating the estimated price change for a bond with positive convexity.
• B) -8.50%, which incorrectly treats the convexity value itself, rather than the properly scaled 0.5 x Convexity x (Δy)^2 term, as directly additive to the duration effect.
• C) -7.08%, calculated as %ΔP ≈ [-Duration x Δy] + [0.5 x Convexity x (Δy)^2] = [-7.5 x 0.01] + [0.5 x 85 x (0.01)^2] = -0.075 + 0.00425 = -0.07075, or approximately -7.08%.
• D) -0.75%, which incorrectly fails to convert the 100 basis point yield change into decimal form (0.01) when applying it to the duration term, effectively treating it as a 1 basis point rather than 100 basis point change.

Question 35

Given a 1-year spot rate of 4.0% and a 2-year spot rate of 5.0%, the implied 1-year forward rate one year from now (the '1y1y' forward rate) is closest to:

• A) 5.00%, which incorrectly assumes the forward rate must simply equal the 2-year spot rate itself, ignoring the compounding relationship with the 1-year spot rate.
• B) 6.01%, calculated from (1 + s2)^2 = (1 + s1)(1 + f), so f = [(1.05)^2 / 1.04] - 1 = [1.1025 / 1.04] - 1 = 1.060096 - 1 = 6.01%.
• C) 6.00%, which incorrectly uses a simple average-based approximation (2 x 5.0% - 4.0%) rather than the correct compounding (geometric) relationship between spot and forward rates.
• D) 1.00%, which incorrectly reports only the simple arithmetic difference between the two spot rates (5.0% - 4.0%) rather than deriving the properly compounded forward rate.

Question 36

A 2-year annual-pay bond has a coupon rate of 5% and a face value of $100. The current spot rate curve shows a 1-year spot rate of 4.0% and a 2-year spot rate of 5.0%. Using the arbitrage-free (spot rate) valuation approach, the bond's value is closest to:

• A) $100.05, calculated as [$5 / (1.04)] + [$105 / (1.05)^2] = $4.808 + $95.238 = $100.05.
• B) $100.00, which incorrectly assumes the bond must trade exactly at par simply because its coupon rate (5%) equals the 2-year spot rate, ignoring the effect of the lower 1-year spot rate on the first cash flow's discounting.
• C) $95.24, which incorrectly discounts the entire $105 final cash flow using the 2-year spot rate but omits the present value of the first year's $5 coupon payment entirely.
• D) $101.85, which incorrectly discounts both cash flows using only the 1-year spot rate of 4.0% rather than applying each cash flow's own maturity-matched spot rate.